| 1. | The existence and stability of the solution of a class of unstirred chemostat model
模型正解的存在性与稳定性分析 |
| 2. | Chemostat model is one of the most significant models in mathematical biology
恒化器模型是生物和数学中非常重要的模型之一。 |
| 3. | Then one can easily obtain the existence of periodic solution of the chemostat model
然后在一致持续生存的条件下得到了该系统周期解的存在性。 |
| 4. | The chemostat is an important device used for growing micro - organisms in a continuous cultured environment , and a medium of great importance between principles and applications
利用恒化器连续培养微生物已是微生物学研究中的一项重要的研究手段；是原理和应用之间的一个极其重要的中介。 |
| 5. | Finalh . the asymptotic behaviour of the chemostat model with two - nutrient and diffusion is further studied . the global attractivity of the periodic solution is proved under the unique existence of the periodic solution
然后进一步研究具有周期环境的双营养扩散恒化器模型的渐近性态，在周期解存在唯一的条件下证明了该周期解的全局吸引性。 |
| 6. | Moreover , under those conditions , the global stability of the positive equilibrium is proved for the two models without delays . iii ) the asymptotic behaviour of the chemostat model with predator - prey populations and delays is studied
三、研究了单营养食物链的恒化器模型的渐近性态，利用波动引理给出了边界平衡点全局吸引性的充分条件。 |
| 7. | In the light of the recent work in biological models , especially in the chemostat models , the dissertation provides a systematic study on the asymptotical behaviour of some chemostat models built by delay or diffusion differential equations . the main contents and results in this dissertation are as follows : i ) the global asymptotic behavior of the chemostat model with the beddington - deangelies functional responses and time delays is studied . the conditions for the uniform persistence of the competing populations are obtained via uniform persistence of infinite dimensional systems
本论文基于当前生物学模型，特别是恒化器模型的研究现状，深入系统的研究了时滞和扩散方程描述的几类恒化器系统的渐近性态，本文的主要内容包括以下几个方面：一、研究了具有beddington - deangelies功能性反应函数的时滞恒化器模型，利用无穷维连续动力系统的一致持续生存的理论给出了两竞争种群一致持续生存的充分条件，利用单调动力学系统得到了系统的全局渐近稳定性。 |
| 8. | Our results imply that mutual interference in a species may result in coexistence of the two competing species and demonstrate that those time delays do not influence the competitive outcome of the organisms . ii ) the asymptotic behaviour of the chemostat model with mutual interference or without mutual interference is studied . for the two models with delay , the uniform persistence of the models are both proved under the conditions of the existence of the positive equilibrium
二、研究了无种内竞争和有种内竞争的具有阶段结构的时滞恒化器模型的渐近性态，对于两类模型，都在正平衡点存在性的条件下证明了该系统的一致持续生存，对于两类相应的常微系统的模型，均在正平衡点存在性的条件下证明了该正平衡点的全局稳定性。 |
| 9. | In this paper we study the single - species chemostat model with time dilay . based on [ 8 ] , we analyze the hopf bifurcation of the system which take the diluton as a parameter , and we obtain that under the conditon of the existence of positive equilibrium and if the dilution is too big or too small , the system will appear hopf bifurcation
在文[ 8 ]的基础上，以模型中的流量为参数进行了hopf分支分析。得出了在正平衡点存在的条件下，当流量较大或较小时，系统的正平衡点附近会产生hopf分支，并应用中心流形和规范形理论给出了分支方向及分支周期解稳定性的计算公式。 |
